Tidecoin uses FALCON as the signature algorithm for the signature. FALCON uses a lattice-based approach.
This article aims to briefly outline what mathematical problem is behind the encryption and why it is so powerful, also against quantum computers
Two vectors are given.
![](https://tidecoin.co/wp-content/uploads/2023/01/lattice_1-300x31.png)
Integer numbers are used for the factors z. Therefore, a grid structure (lattice) results. Hence the name lattice based encryption. You can see an illustration in the document.
![](https://tidecoin.co/wp-content/uploads/2023/01/lattice_based_cryptography-768x700.png)
Let us try an example with real values for the vectors b.
![](https://tidecoin.co/wp-content/uploads/2023/01/lattice_2-300x40.png)
The following vector is now choosen randomly. Constraint is, it must not be a multiple of the vector equation and the vector must be an integer.
![](https://tidecoin.co/wp-content/uploads/2023/01/lattice_3.png)
The goal is to find the smallest distance to the vector for the given points from the upper lattice structure (closest vector problem). We can set up a system of equations for this. However, we notice that we have two variables and two equations. So it might be easy to solve by using a calculator.
Both values for z must be rounded to an integer so that we end up on a grid point after solving the equation.
![](https://tidecoin.co/wp-content/uploads/2023/01/lattice_5-300x37.png)
We are calculating the grid point with the rounded values for z and the vectors.
![](https://tidecoin.co/wp-content/uploads/2023/01/lattice_6-1024x103.png)
The calculated lattice point is far away and certainly not the nearest neighbor of the choosen vector (27, 8).
Even if we substitute z1 = 1 and z2 = 0 from our considerations, we get (37, 41) as a lattice point. This lattice point is closer than the calculated point.
This mathematical problem is very difficult to solve. Quantum computers will have no advantage over analogue computers here.
Lattice-based encryption, including the FALCON signature, is based on this approach.
FALCON is used by Tidecoin to protect wallets from attacks by the quantum computer.